Third lecture
More on Reference-Dependent preferences.
First some leftovers from last week: Since the paper is a bit complex, I here present at
simplified version of:
Köszegi, B and M. Rabin (2006): A Model of Reference-dependent Preferences, Quarterly
Journal of Economics, CXXI.
They consider multiple goods, we consider only two. There is a standard utility function,
measured in monetary units, the simplest case is when it is separable, m(c)=m1(c1)+ m2(c2).
(Note that a Cobb-Douglas written with logarithms satisfies this m(c)=a ln(c1)+ b ln(c2).)
Total utility includes a loss-gain term n(c|r), this is also separable. Thus total utility is:
u(c | r )  u1 (c1 | r1 )  u2 (c2 | r2 ) where
ui (ci | ri )  mi (ci )  n(ci | ri ) for i  1,2
The loss gain term corresponds to the value function in prospect theory, but we only care
about loss aversion, that is the kink. That is we drop weights that differs from probabilities
and we drop the concavity-convexity part of the value function, and assume it is linear, except
for the kink. Using Köszegi and Rabin’s notation, the value function would be.
 ax
when x  0
 ( x)  
and where 0  a  1 and   1, (for concreteness think   2)
 ax when x  0
Köszegi and Rabin transfers everything into money (using m(c) rather than c) before applying
this function, and hence
n(ci | ri )   (mi (ci )  mi (ri )) for some constant a.
The equilibrium.
Consider a consumer that has to choose between two lotteries, call them F and G. You can
think of F as planning to buy a pair of shoes when you do not yet know the price (two
possible prices, with equal probability. G is planning not to buy any shoes. In this case G is no
real lottery as the outcome in terms of both shoes and money is certain.
Suppose you plan to buy the shoes; this will then be the reference point. Note that r in this
case is uncertain. There are two possible outcomes in terms of how much you pay in the
reference point. You must compute utility for both reference point and weigh with
probabilities.
Personal equilibrium: If you plan to buy the shoes, this will be the reference point. If buying
the shoes give higher utility – given this reference point – than not buying the shoes, then the
plan to buy the shoes is rational, and it constitutes a personal equilibrium. If not to buy is
optimal when buying is a reference point, then buying is not a personal equilibrium.
The endowment effect:
The classical experiments on the endowment effect is presented in
Kahneman, D., J. Knetsch, and R. Thaler (1990). "Experimental Tests of the Endowment Effect and
the Coase Theorem," Journal of Political Economy, 98, 1325-1348.
You do not have to care about the Coase Theorem, just try to get a grip on what the endowment
effect is and what kind of experiments are used to document the effect.
The endowment effect has been challenged by Plott and Zeiler. You do not have to understand all
the details of their experimental design, but try to figure out how their design differ from the
traditional ones. Hint: What do they mean by the terms “practice” and “training”? What is Plott and
Zeilers explanation of why Kahneman et. al. found an endowment effect?
Plott, C. R and K. Zeiler (2005). "The Willingness to Pay-Willingness to Accept Gap, the “Endowment
Effect,” Subject Misconceptions and Experimental Procedures for Eliciting Values," American
Economic Review, 95, 530-545.
Rabin’s Theorem
) be the utility of a person where W is initial wealth and x
This is about expected utility. Let (
is the gain from a lottery. As I’ll explain in class, we may choose the utility function such that
( )
)
, and (
. Now suppose the person is offered a lottery
+100 Kroner
-100 Kroner
With probability 2/3
With probability 1/3
(
The expected utility of this lottery is
)
(
). Suppose the person is
indifferent between this lottery and no gambling at all which gives wealth W for certain. That is;
utility is u(W). Since he is indifferent,
(
Using that
( )
)
, and (
)
(
Compute (
(
)
( )
this can be written
(
)
)
).
The person is still indifferent even if we increase his wealth with 100 kroner. Why does this imply
that
( )
(
)
(
)
1/29/2013
ECON4260 Behavioral
Economics
3rd lecture
Endowment effects
and
aversion to modest risk
The endowment effect
• Three groups:
– Mug owners get at mug (worth 5$ at the local store)
– Buyers get 5$
– Choosers get nothing, but will choose money or cup.
• Elicit willingness to pay / willingness to accept
– The mug owners will sell for 7.12 $
– The others will buy for 2.87 $
– The choosers indifferent at 3.12 $
• Prospect theory interpretation
– Getting the mug makes it a loss to part with it
– The mug is a gain if you have not been given one
Exchange
• Half the group get the mug
– Independent of mug-valuation
• The 50% with highest mug valuation will be
divided:
–
–
–
–
One half got a mug
The other half did not
Expect half the mugs to be traded
Actually about 10-20% are traded
• Coase’s theorem: Final allocation independent
of initial assignment of property rights
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Transaction costs
• Same experiment with poker chips
• Each participant has a given ”exchange rate”
• If it is worth 5$ to me and 3$ to you both will
benefit if you sell it to me for 4$.
• Demand and supply functions derived
• Can find market equilibrium prediction,
provided no transaction costs.
• RESULT: Outcome equals prediction
• No transaction cost
Endowment effects in
The Edgeworth box
• Crossing indifference
curves
Pens
P for M
– Pens for Money
– Money for Pens
M for P
Dollar
• Kinked indifference
curves around status
quo
• E.g. the Edgeworth
box
The evolution of endowment effect
• Animals face recurrent
fights over resources
• A coordination game,
need a coordination
device
• Incumbent stay, entrant
runs
• Butterfly experiment
– Both on hilltop for one day
– They fight (both incumbents)
• Fighting over a resource
– Two Nash equilibriums (ESS)
– One fight and one run
• Both fighting, they’ll kill
each other
• Allow some initial test of
strength
Fight
Run
Fight
-1,-1
1,0
Run
0,1
0,0
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Plott and Zeiler’s critique of the
”endowment effect’
• Is the WTP/WTA gap really evidence of an endowment
effect?
•
•
•
•
WTP/WTA not found in all studies
Differences in procedures
The results depend on procedures
Concern about misunderstanding
– Do subject understand ”true value”
• Anonymity
– Do high-bidders apear naive?
Becker-DeGroot-Marschak
mechanism
• How much will you accept to part with the mug?
– Say you’ll really do it for 5$
– Why not state 7$ and hope you will get at least 6$
• BDM-Mechanism (seller)
–
–
–
–
The seller states a minimum price X (Your state 7$, true price is 5$)
A random price P is drawn (Suppose we pick 6$)
Sold at price P if P≥X (If you stated 7$, you lost the 6$ deal)
The mechanism is incentive compatible. (Rational to state 5$)
• Do subject understand the incentive compatibility?
– Or do they still try to sell high and buy low?
Misconceptions
• ”Revealed theory approach”
• 4 Controls
–
–
–
–
Incentive compatibility
Training
Paid Practice
Anonomity
• Situation trigger ”selling behavior”, i.e. selling high.
• Not fully understand auction mechanism
– Behave as if an standard acution.
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Design and results
• Invoke all controls
– Training, paid practice, incentives (BDM) and anonymity
• Main result: No WTA-WTP gap
– That is: No Endowment effect
– True even without paid practice
• What about exchange-effect
– Not in the paper
– Plott and Zeiler in later paper: Remove the word ”gift” and the
exchange effect disappear.
Does Plott and Zeiler show that
prospect theory is wrong?
• The paper demonstrates a problem with the intial
experimental design.
 The effect does depend on experimental procedures
• An alternative interpretation
 Training induces expectations of trade and hence influence the reference
point.
 Still, original studies no longer provide evidence of an endowment effect,
may just as well be misconceptions
• Unrelated evidence for reference points
 The study of working with 50-50 (fixed effort based payment)
 Importance of status quo
 But can also be effort, coordination or implicit endorsement
 Effect of reframing in Kahneman and Tversky (+2000 the loss / only gain)
Raise your hand if you disagree
Suppose that you prefer lottery A to lottery B
You are then offered lotteries C and D
C: Flip a coin and you get A if head (otherwise 0)
D: Flip a coin and you get B if head (otherwise 0)
It is rational to prefer C to D, as the lottery you get if
head is then preferable (A better than B)
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1/29/2013
Rabin’s Theorem
A teaser
• How many of you would participate in the following
lotteries (the alternative is (0)).
– A: (-100, 33 %, +100, 67 %)
– B: (-100, 45 %, +100, 55 %)
• Would changes in wealth (±10 000 kroner) affect
your preferences?
• If you decline A (B), or were indifferent, then the
logical implication is to decline C (D):
– C: (-100, 50 %, +10 billions, 50%)
– D: (-100, 85 %, +10 billions, 15%)
Rabin’s theorem
• Suppose a person is indifferent to (0) and a lottery
(+100 Kr , 67% ; -100 Kr , 33%)
• The person would be indifferent irrespective of
income level
• Assume the person maximizes expected utility
• For what values of X will he prefer the lottery (X ,
50% ; -100 , 50%) to (0)?
Lotteries and wealth
• xi is payoff from a lottery
• The subject has additional wealth and income
W.
• The lottery changes the total wealth from W to
W+xi
• Expected utility should thus be written
n
Eu (W  x)   u (W  xi ) pi
i 1
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Indifference for any W
• Indifference implies
(2/3) u(W + 100) +
(1/3) u(W -100)
= u(W)
Du+=u(W+100)-u(W)
Du-=u(W)-u(W-100)
Du-= 2 Du+
12
11,5
11
10,5
10
9,5
1
2
3
12,5
12
11,5
11
10,5
10
9,5
9
1
2
3
4
5
6
7
8
9
10 11 12
Sketch of proof
• u(W+300) = u(W+300)-u(W+200)
+ u(W+200)-u(W-100)
+ u(W+100)-u(W)
= Du+/4 + Du+/2 + Du+
• u(W+ n 100)-u(W) = (1+2-1+ …+2-(n-1)) Du+ <
Du• Eu = 50% u(W+ n 100)+50%u(W-100)
• Eu-u(W)= 50% [u(W+ n 100) - u(W)]
- 50% [u(W) – u(W-100)] < 0
Almost any risk aversion
yields similar results
• A person who turns down a lottery
(100, 51%;-100,49%) at any income level
• Will also turn down
(+10 000 000 000, 51%, -1 800, 49%)
• If such conclusions are implausible, EU imply risk
neutrality towards modest risk.
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Indifference for W < W0+10 000
• Is the problem that the
person is indifferent for
any level of W?
• With W0 = 1 000 000,
12 in the figure is only
1 001 200
• Turn down
(-100,55%;1.4 1031,45%)
12,5
12
11,5
11
10,5
10
9,5
9
1
2
3
4
5
6
7
8
9
10 11 12
Prospect theory, by contrast,
yields modest risk aversion
• Reference point is current
wealth.
• Choices should be
independent of wealth
– Plausible?
– Could you think of an
experiment to test it?
– Can the theory easily be
adjusted to account for
wealth?
• Loss aversion implies risk
aversion even for modest
risk.
Default / Status Quo Bias
• Samuelson and Zeckhauser (1988):
– A: ”…You inherit a large sum of money from your uncle. …”
– B: ”… You inherit a portfolio… A significant portion invested in
modest risk company. …”
– The choice: Moderate risk company; high risk company, treasury
bills, municipal bonds.
– Result: An option is more likely to be selected when it is designed
as the status quo.
• Organ donations
• Saving for retirement (opt in or opt out)
• Choosing the first dish in display
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Explaining default effects
• Effort
– Becoming a organ donor requires effort (as does opting out)
• Implicit endorsement
– I ask “does anybody disagree”, it may have been interpreted as
“you better not”.
• Coordination
– “Raise your hand” may be a coordination game
– “I want to answer the same as everyone else”
– “Nothing” is the best prediction of what others will do
• Besides, I can raise may hand after the others
• Loss aversion
– It is often natural to expect status quo.
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Fairness
• Q 1a: “A shortage has developed for a
popular model of automobile, and customer
must wait two months for delivery. A dealer
has been selling the car at list price. Now the
dealer prices the model 200 $ above list
price”
– Acceptable (29%)
Unfair (71%)
• Q 1a: “... A dealer has been selling the car
200 $ below list price. Now the dealer prices
the model at list price
– Acceptable (58%)
Unfair (42%)
Liberal paternalism
• We need defaults
–
–
–
–
Organ donor or not?
Many left without a license when they had to choose (no default)
Join savings plan or not
There is some food on the first spot
• It is easy to opt out – no one forced (Liberalism)
• Knowing that more people pick the first dish
– Should the healthy or unhealthy be picked first? (Paternalism)
• Caveat
– Suppose one option is good for society another for the individual
• Littering, military services…
– Is it acceptable for the government to induce individuals to act
against their own self interest, using subtle means like: defaults?
Økonomisk institutt
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